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Ogila et al. – eXPRESS Polymer Letters Vol.11, No.10 (2017) 778–798 2.2.1. Front tracking model This is a dual-phase kinetic model in which the poly- mer melt and powder layers (or polymer melt and solid layers during cooling) are separated by an in- terface. The powder layer melts when the tempera- ture at the interface (Ti) reaches polymer melting temperature (Tm). As melting proceeds the interface moves the from the mold surface through subsequent powder layers until all of the powder is melted [11]. During cooling a similar process occurs at the inter- face as Ti approaches the crystallization temperature (Tc) at each consecutive interface position. Early proponents of this method include Rao and Throne [12]; whose work considered the complex tumbling of powder particles within the mold in its description of heat transfer. The model showed poor correlation with experimental results. Improvements by Throne [13] suggested that the powder mass be considered static in the mold (static bed), ignoring the complex powder kinetics. The simplified model had much better agreement with experimental re- sults. This early success resulted in a slew of works that applied the front tracking model [11, 14–19]. However, the front tracking model is complicated and its implementation especially tedious due to the additional boundary conditions that must be satisfied at the melt/powder interface; and the necessity to track the position of this interface as it moves from the mold surface through the powder thickness [11, 17]. Another difficulty is the poor representation of the pseudo plateaus of melting and crystallization. Because Ti is taken to be constant (i.e. equal to either Tm or Tc), solving of the thermal balance equation generates a constant temperature plateau at points associated with phase change [12–16]. Employing a discreet number of Tm results in marginal improve- ments [18, 19]. Gogos and coworkers [11, 17] assumed a well-mixed powder as a result of the tumbling action during mold rotation. The temperature of the powder was uniform across its volume and increased evenly with time. Numerical results more closely resembled those ob- tained empirically; however, due to the well mixed as- sumption, internal air temperatures (IAT) increased much slower than expected. 2.2.2. Fixed domain model Proponents of the fixed domain point to the shortcom- ings of the front tracking model as the main merits of their method. Indeed, this model does not require the application of a melt powder interface; and by ex- tension the boundary conditions that are required in order to define it [8]. The models currently being in- vestigated for RM can be divided into temperature based [10, 20, 21], source based [22] and enthalpy- based [23–26]. In this instance as well the main dif- ference between them is the manner in which ∆H is represented. Lim and Ianakiev [10, 20] presented the energy equa- tion of the bulk air inside the mold as a lumped pa- rameter system that they combined with a coincident node technique and Galerkin finite element method (FEM). The model predicted the stratified deposition of polymer melt onto the mold wall, and although successful in capturing polymer phase change, it pre- dicted an earlier shorter and less pronounced pseudo plateau of melting when compared with experimen- tal results. The numerical melting phase proceeded faster than expected, which could not be accounted for by the layer-by-layer deposition. Banerjee et al. [22] incorporated into Equation (1) the latent heats of melting and crystallization as a sink/ source term respectively (Equation (2)): 2m DH=tpHm 2t (2) where ρpHm is the latent heat per unit volume, and ∂λ/∂t is the melting rate. As a result of the imperfect contact between itself and the mold, the tumbling powder was heated by convection and heat transfer in the powder mass oc- curred by conduction only. A finite difference scheme discretized the governing equations and boundary conditions. The model predicted the layer-by-layer deposition of the melt in good agreement with ex- periments. For the enthalpy based models two approaches are encountered in literature Sarrabi et al. [8] and Tcharkhtchi et al. [27] presented a non-empirical so- lution for Equation (1) derived from the Law of global enthalpy change with temperature. A finite differ- ences scheme discretized the core equations of the model using a first order implicit Euler algorithm. The model represented the pseudo plateau of melting well; that of crystallization was, however, unsatisfac- tory. The authors attributed this difference between numerical and experimental results to crystallization kinetics; which their model did not account for. The second approach encountered [23–26] is the ex- pression of the total phase transition enthalpy as 780PDF Image | Rotational molding: A review
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